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Let's solve the composite functions step by step based on the provided information.

We are given the following functions:
- \( f(x) = x^5 \)
- \( g(x) = \sin(x) \)

### 1. \( f(g(x)) \)

The composite function \( f(g(x)) \) means applying \( g(x) \) first, and then applying \( f(x) \).

\[
f(g(x)) = f(\sin(x)) = (\sin(x))^5 = \sin^5(x)
\]

So, the answer for \( f(g(x)) \) is:

\[
f(g(x)) = \sin^5(x)
\]

---

### 2. \( g(f(x)) \)

The composite function \( g(f(x)) \) means applying \( f(x) \) first, and then applying \( g(x) \).

\[
g(f(x)) = g(x^5) = \sin(x^5)
\]

So, the answer for \( g(f(x)) \) is:

\[
g(f(x)) = \sin(x^5)
\]

---

Would you like further details or explanations on any part of this process?

Here are some related questions to expand on this topic:

1. How do you find the derivative of composite functions like \( f(g(x)) \)?
2. What is the chain rule, and how is it applied in differentiating composite functions?
3. How do you calculate the inverse of composite functions?
4. Can you simplify \( f(g(x)) \) for more complex functions, like trigonometric compositions?
5. How do composite functions apply in real-world scenarios, such as physics or engineering?

**Tip:** When working with composite functions, it's useful to think of each function as a transformation applied in a specific sequence. This helps keep track of which function to apply first.

Let f(x) = x^5 and g(x) = sin(x), give the following composite functions: f(g(x)) and g(f(x))

Learn how to solve composite functions using f(x) = x^5 and g(x) = sin(x). This tutorial includes detailed solutions for f(g(x)) = sin^5(x) and g(f(x)) = sin(x^5). Suitable for high school students in Grades 10-12.

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